Question

PQRS is a cyclic quadrilateral. Given $\angle$QPS $={73}^o$, $\angle$PQS $={55}^o$ and $\angle$PSR $={82}^o$, calculate $\angle$PRQ.

Answer 1

In $△PQS$

$\angle QPS+\angle PSQ+\angle PQS={180}^o$

$\Rightarrow \angle PSQ={180}^o-({73}^o+{55}^o)={52}^o$

Since $\angle PSQ$ and $\angle PRQ$ are in the same segment of the circle, they must be equal.

Therefore, $\angle PRQ={52}^o$